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I ran into this slight inconvenience. I needed to know where a certain variable was used throughout my C program. But the variable name also existed in comments. Which made the search more cumbersome

It would be a nice addon for Kate that Kate recognizes variables and perhaps other keywords as well so one can easily every reference to a certain variable.

Or alternatively an option which lets the search function ignore commented texts.

I think that's what the CTags plugin is for, or at least helps with.
For more advanced functionality, you might consider using Kdevelop instead.